Chapter Eight-Energy

8.1: Work

When the object moves parallel to the direction of the force, the force is doing work

Work is a produce of force and distance (W=Fd), measured in joules (J)

Examples: Bobby pushes his grandma with 3 newtons of force. If he pushes her a distance of 4 meters from him, how much work is he exerting on grandma?
(3 N)(4 M)=12 J

If grandma moves Bobby a distance of 3 meters and exerts 18 J of work, how much force is she exerting on Bobby?
W/D=F (18 J)/(3 M)=6 N

8.2: Power

The speed at which work is done

W done/Time interval= Power (P=W/t)

Measured in watts (W), (J/s)

Examples: Willy exerts 100 J of work on his dog sled team. If it takes him 20 seconds to get to the finish line, how much power is he exerting?
(P=W/t) (100 J)/(20 s)=5 W

Susan B. Anthony is traveling a distance of 52 meters on her horse and buggy (the horse exerting 7 N of force.) If she travels at this rate for 10 seconds, how much power is her horse exerting?
W(Fd)/t=P
(52 M)(7 N)/(10 s)=36.4 W

8.3 :Mechanical Energy

Energy-total amount of work done in an object, measured in joules

Two types of mechanical energy: kinetic and potential

8.4 Potential Energy

The energy the object stores when it is lifted to a higher position.

PE=mg(weight)h(distance the object goes)

It is a relative measurement, so you get to pick the height that will be your "zero level", just keep it the same throughout your calculations.

Examples:
Roger throws Harold (Harry, if you please) in the air a distance of 8 meters. If Harold weighs 81 kg, what is his potential energy?
PE=mgh
(81 kg)(10 m/s)(8 m)=6,480 J

8.5 Kinetic Energy

Energy in motion that equals the work done in making the object reach the speed that you are calculating the kinetic energy for

The more mass or speed the object has, the larger the kinetic energy

KE=1/2mv²

Examples:
Lucy's mass is 8 kg. If she rolls down a hill with a velocity of 12 m/s, how much kinetic energy will she produce?
KE=1/2mv²
1/2(8 kg)(12 m)² =576 J

Example:
Willfred's kinetic energy is 370 J. If his mass is 87 kg, what is his velocty?

370=1/2(87)v²

v=2.94 m/s

8.6 Conservation of Energy

Law of conservation of energy- states that energy cannot be created nor destroyed, only transfered from object to object or transformed to a different type of energy within the object.

The total amount NEVER changes
In the absence of friction:
PEi + KEi = PEf + KEf
or
mghi + 1/2mv²i = mghf + 1/2mv²f

Example:
If you have a mass of 80 kg and run towards a wall at 15 m/s² and jump up one meter to kick it, how much energy must the wall get according to the conservation of energy?

(80 kg)(10m/s)(1 m) + 1/2(80kg)(15m/s²)=1400 J

8.7 Machines

A machine multiplies forces or changes their directions to make your job easier. No machine can make or destroy energy (conservation of energy).

Ideally, when no work is lost to friction:

Wout = Win
or
FoutDout = FinDin

Mechanical advantage is when the machine multiplies the force you put in to get the work it puts out.

MA=Fout/Fin

When there is no friction, the theoretical mechanical advantage is expressed as the ratio of the input and output distances

TMA= din/dout

8.8 Efficiency

The ratio of input and output work is better known as efficiency.

eff= Wout/Win
or
eff= MA/TMA

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